with the (time-dependent) granular temperature \(T_g = \frac{2}{\mathfrak {D}}\frac{K(t)}{N}\) , i.e., twice the kinetic energy per
particle per degree of freedom, while \(T = (\mathfrak {D}/2)T_g/m\) 
is the square of the velocity fluctuations.
The diameter of the particle is \(d\) , \(\nu \)  is
the packing fraction of the system and \(m\)  the mass of the
particles.
In 2D, the pair correlation
function at contact \(g_{\mathfrak {D}}\)  is given, approximately for low
to moderate densities, by [1]}, [2]}
\(g_2(\nu ) =\frac{1-7\nu /16}{(1-\nu )^2}~,\) 
